A Parallel Primal-Dual Interior Point Method for Multi-Period and Multi-Facility Production Planning Problems

Abstract

A parallel implementation of a primal-dual interior point method is presented for multi-period and multi-facility production planning problems with nonlinear constraints. Exploiting the nested primal block-angular structure of the problem, the system of linear equations for calculating the search direction is decomposed into independent systems of linear equations and another system of linear equations which can be solved efficiently owing to the staircase structure of the coupling constraints. Computational experiments on the parallel computer VPP800 shows that the proposed method is very efficient for large-scale multi-period and multi-facility production planning problems.